Weniger%20transformation
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1: 1.14 Integral Transforms
§1.14 Integral Transforms
►§1.14(i) Fourier Transform
… ►§1.14(iii) Laplace Transform
… ►Fourier Transform
… ►Laplace Transform
…2: Bibliography W
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Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series.
Computer Physics Reports 10 (5-6), pp. 189–371.
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Computation of the Whittaker function of the second kind by summing its divergent asymptotic series with the help of nonlinear sequence transformations.
Computers in Physics 10 (5), pp. 496–503.
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Rational approximations for the modified Bessel function of the second kind.
Comput. Phys. Comm. 59 (3), pp. 471–493.
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A rational approximant for the digamma function.
Numer. Algorithms 33 (1-4), pp. 499–507.
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Asymptotic Approximations to Truncation Errors of Series Representations for Special Functions.
In Algorithms for Approximation, A. Iske and J. Levesley (Eds.),
pp. 331–348.
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3: 3.9 Acceleration of Convergence
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§3.9(i) Sequence Transformations
… ►§3.9(v) Levin’s and Weniger’s Transformations
… ►In Weniger’s transformations the numbers in (3.9.13) are chosen as follows: …See Weniger (1989). … ►For applications to asymptotic expansions, see §2.11(vi), Olver (1997b, pp. 540–543), and Weniger (1989, 2003).4: 2.11 Remainder Terms; Stokes Phenomenon
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►For a comprehensive survey see Weniger (1989).
►The following example, based on Weniger (1996), illustrates their power.
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►For example, using double precision is found to agree with (2.11.31) to 13D.
►However, direct numerical transformations need to be used with care.
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5: 10.76 Approximations
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►Luke (1971b, a, 1972), Luke (1975, Tables 9.1, 9.2, 9.5, 9.6, 9.11–9.15, 9.17–9.21), Weniger and Čížek (1990), Németh (1992, Chapters 4–6).
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6: 20 Theta Functions
Chapter 20 Theta Functions
…7: 5.23 Approximations
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►For additional approximations see Hart et al. (1968, Appendix B), Luke (1975, pp. 22–23), and Weniger (2003).
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8: 20.10 Integrals
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§20.10(i) Mellin Transforms with respect to the Lattice Parameter
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20.10.1
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20.10.2
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20.10.3
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§20.10(ii) Laplace Transforms with respect to the Lattice Parameter
…9: Bibliography N
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On an integral transform involving a class of Mathieu functions.
SIAM J. Math. Anal. 20 (6), pp. 1500–1513.
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On an asymptotic expansion of the Kontorovich-Lebedev transform.
Applicable Anal. 39 (4), pp. 249–263.
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On an asymptotic expansion of the Kontorovich-Lebedev transform.
Methods Appl. Anal. 3 (1), pp. 98–108.
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Reduction and evaluation of elliptic integrals.
Math. Comp. 20 (94), pp. 223–231.
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A table of integrals of the error functions.
J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.
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10: Bibliography F
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Sur certaines sommes des intégral-cosinus.
Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
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Tables of Elliptic Integrals of the First, Second, and Third Kind.
Technical report
Technical Report ARL 64-232, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio.
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On the asymptotic expansion of Mellin transforms.
SIAM J. Math. Anal. 18 (1), pp. 273–282.
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On weighted polynomial approximation on the whole real axis.
Acta Math. Acad. Sci. Hungar. 20, pp. 223–225.
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